3Definition  (Restricted secant inequality (RSI) [1]})  
The set of functions satisfying the restricted secant inequality with parameter \(C\) , denoted \(\mathrm {RSI} (C)\)  is defined as follows. A function \(g : \mathbb {R}^m \rightarrow \mathbb {R}\)  belongs to \(\mathrm {RSI} (C)\)  iff for some \(z^* \in \operatornamewithlimits{arg\,min}_{z \in \mathbb {R}^m} g(z)\)  and for all \(z \in \mathbb {R}^m\) ,
\(\langle \nabla g (z), z^* - z \rangle \ge C \Vert  z^* - z \Vert _2^2.\) 

